Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
```        A sky lab of mass m kg is first launched from the surface of the earth in a circular orbit of radius 2R and then it is shefted frm this circular orbit to another circular orbit of radius 3 R. Calculate the energy required :-
(a) to place the lab in the first orbit.
(b) to shift the lab frm first orbit to the second orbit. (R = 6400 km, g= 10 m/s2)```
7 years ago

23 Points
```										Dear Sanchit,
The energy required to launch a sky lab is the sum of thenergy required to take the lab to that height and the kinetic energy given to it launch in the orbit.
(a)Now the energy required to take the lab to a given height is nothing but the change in the potential energy of the lab
so ΔPE = U(2R) - U(R) = - GMm/2R + GMm/R = GMm/R
now the velocity given to the lab is calculated from the fact that the gravitational force is balanced by centripetal force
mv2/2R = GMm/(2R)2
this gives v= √(GM/2R)
thus the kinetic energy given to it is KE=  m v2/2 = mGM/4R
thus the total energy required to launch into the orbit of 2R radius is ΔPE + KE = 5GMm/4R
(b) Now the total energy of the lab in th orbit of 3R radius is calculated in the similar fashion to get a value of 5GMm/6R
Thus the energy required for this shift is difference of the two total energies = 5GMm/12R
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.
All the best!!!

Regards,
```
7 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Mechanics

View all Questions »
• Complete Physics Course - Class 12
• OFFERED PRICE: Rs. 2,756
• View Details
• Complete Physics Course - Class 11
• OFFERED PRICE: Rs. 2,968
• View Details